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Combustion Wave Structure of Hydroxylammonium Nitrate Aqueous Solutions

Toshiyuki Katsumi* and Keiichi Hori† Institute of Space and Astronautical Science (ISAS/JAXA), Sagamihara, Kanagawa, 252-5210, Japan

and

Ryuta Matsuda‡ and Tomo Inoue§ Tokai University, Hiratsuka, Kanagawa, 259-1292, Japan

The combustion characteristics of hydroxylammonium nitrate aqueous solution were studied. It was found that the role of the two-phase region is very important and the boiling of water by superheat is responsible for the high burning rate. The evaluated bubble nucleation rate coincides with burning rate at very high region. Further, the combustion mechanism of propellant solution is discussed. The hydrodynamic instability was taken into the discussion, and the estimation of hydrodynamic instability supports the observed phenomena. These discussions of hydrodynamic instability and bubble nucleation solution are summarized, and the combustion mechanism of the propellant solution is described in detail.

Nomenclature Ap = pressure sensitivity dn/dt = bubble nucleation rate dv/dt = increase rate of nucleus volume per unit volume Fr = Froude number ifg = latent heat of vaporization k = Boltzman constant Ka = Karlovitz number Le = Lewis number M = molecular weight Ma = Markstein number Ma(cr) = critical Markstein number N = number of molecules per unit volume pf = pressure in liquid phase rb = linear burning rate R = universal gas constant r* = radius of the spherical vapor nucleus Su(l) = burning rate of laminar flame Su(s) = burning rate of stretched flame T0 = initial temperature Tad = adiabatic flame temperature Tbp = boiling temperature * Postdctoral fellow, Department of Space Transportation Engineering, 3-1-1 yoshinodai, Chuo, Sagamihara, Kanagawa, 252-5210, JAPAN, AIAA Member. † Professor, Department of Space Transportation Engineering, 3-1-1 yoshinodai, Chuo, Sagamihara, Kanagawa, 252-5210, JAPAN, AIAA Member. ‡ Graduate student, Course of Aeronautics and Astronautics, 4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292, JAPAN. § Graduate student, Course of Industrial Chemistry, 4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292, JAPAN.

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit25 - 28 July 2010, Nashville, TN

AIAA 2010-6900

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Td = activation temperature of mass diffusivity in condensed phase Tf = flame temperature Tg = vapor temperature Ts = surface temperature TSAT = saturation temperature β = Zel’dovich number ∆G(r*) = formation energy of bubble radius r* ∆T = superheat; ∆T =Tg-TSAT λ = collision frequency ρ = density ratio ρg = burned gas density ρl = unburned liquid density σ = surface tension

I. Introduction ydroxylammonium nitrate (HAN) based solutions have been considered as candidates for monopropellants and as the liquid oxidizer of hybrid rockets because of their promise in the areas of storability,

environmental/health, propulsion performance, density, and thermal management. However, HAN-based solutions often exhibit extremely high burning rates, and such characteristics sometimes cause serious accidents1. This attribute has unfortunately retarded the use of the solutions in those applications. Recently, methanol addition was found to be effective in suppression of the burning rate. In our previous study2, it was found that a certain range of HAN/ammonium nitrate (AN)/water/methanol compositions exhibit moderate burning rates and excellent properties in specific impulse (Isp), density, viscosity, melting point, and reactivity with catalysts. As a monopropellant, the HAN-based solution has low toxicity, and density*Isp is well above that of hydrazine.

Combustion characteristics and mechanisms of HAN-based solutions have been studied by several researchers over a period of many years. Vosen3, 4 associated the decomposition rates of HAN-water mixtures with the density ratio, ρproduct/ρreactant. In the case of low-density ratios, decomposition rates depend primarily upon the density ratio. In higher ratios, these rates are independent of the density ratio. In addition, the overall burning rate decreases with an increase in pressure up to 26 MPa, which is caused by hydrodynamic instabilities; above 26 MPa, the burning rate is independent of pressure. Chang and Kuo5 assessed the combustion characteristics and mechanisms of the HAN-glycine-water solution for pressures ranging from 1.5 to 14.5 MPa. The slope break point in the curve of the burning rate occurs as the result of a change in the burning mechanism. In another paper, Chang et al.6 studied the combustion characteristics of HAN/AN/water/methanol solutions between 0.74 and 7.3 MPa. Combustion behaviors were influenced by the content of water and methanol, and there was a change in the combustion mechanism at the pressure of the break point. Further, Lee and Litzinger7 studied the chemical kinetics of HAN decomposition. The eight reactions were chosen as the reduced reaction model for HAN decomposition, and the numerically simulated mass fractions of main species in both gas-phase and condensed-phase coincided with the experimental data.

Regardless of these studies, the combustion mechanism still has not been clarified completely, especially the mechanism of inducing the extremely high burning rate of HAN-based solutions. The combustion characteristics of the HAN/AN/water/methanol compositions were studied in our previous study 8 , however the combustion mechanism was not understood fully. Our interest is focused on the combustion characteristics of HAN aqueous solution, because AN and methanol included in the propellant complicates the combustion phenomena. Several samples with HAN concentration ranging from 95 to 50 wt.% were prepared. The linear burning rates of these samples were obtained as a function of pressure; the observation of combustion phenomena was conducted with a medium speed video camera; and the temperature profile of the combustion waves was measured with a 25 microns diameter thermocouple. From these results, it is found that the boiling of water in two-phase region is important for combustion mechanism of aqueous solution. The bubble nucleation rate is evaluated, and the calculated nucleation rate coincides with burning rate at very high region. Based upon these discussions, the combustion mechanism of the aqueous solutions is proposed.

This mechanism of aqueous solutions at high burning rates can be applied to the propellant solutions, however it is not sufficient to get the comprehensive combustion model. In the previous study of HAN-based propellants8, it was found that hydrodynamic instability might be the trigger for the jump to the extremely high burning rate region. Vosen3,4 mentioned about the hydrodynamic instability which occurs lower than 26 MPa, however this does not explain our observed phenomena; combustion wave becomes stable at lower pressure than the critical value, 3-5

H

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Ignition wire

Thermocouple

Two-bore ceramictube

Glass tube

Figure 1. Experimental setup

MPa. Margolis9 showed the stability criteria of the combustion wave based upon the Landau-Levich instability, however this stability criteria dose not met our data. Therefore, another mechanism is necessary and the effect of flame stretch on the hydrodynamic instability is estimated with Markstein number which relates the burning rate to the flame stretch. Based upon the relationship between the pressure dependency of hydrodynamic instability and our data, the critical Markstein number where the burning rate jumps to the very high region is defined and its details are discussed.

II. Experiment and Results

A. Sample and Experimental Setup Seven aquous solutions were prepared in

order to obtain the effects of HAN concentration. The HAN consentrations of aquous solutions are 95, 85, 82.5, 80, 77.5, 64 and 50 wt.%. 95 wt.% is the maximum concentration which can be prepared at room temperature. The sample solution were placed in glass tubes, and burnt in a strand burner purged with nitrogen gas at 1-10 MPa. The initial temperature of the sample solutions was set at 24 °C. The combustion wave of HAN aqueous solutions in the glass tube was observed with a medium speed video camera (at 500 frames per second). The temperature was measured with 25.4 µm diameter type-R (Pt and Pt-13%Rh) thermocouples. The thermocouples were installed in a 12mm diameter glass tube, as shown in Fig. 1.

B. Linear Burning Rate Linear burning rates of 95, 85, 82.5 and

80 wt.% solutions are shown in Fig. 2. Comparison with the data of HAN crystal by Kondrikov et al10. is also made. The burning rates increase as the HAN concentration decreases down to 80 wt.%. The burning rate of 95 wt.% is nearly same as that of HAN crystal. Linear burning rates of 80, 77.5, 64 and 50 wt.% solutions and the data of 64 wt.% by Kondrikov et al. are shown in Fig.3. The burning rates decrease as the concentration decreases in this group. The burning rate of the 64 wt.% solution coincides with the data by Kondrikov et al. From Figs. 2 and 3, the linear burning rate peaks at around 80 wt.% HAN concentration. At the high burning rate zone, more than 100 mm/s, the burning rates do not depend on pressure.

C. Observation of Combustion Phenomena

The linear burning rates range from several millimeters per second to several hundred millimeters per second, and can be classified into three regions - high, medium and low burning rates. The combustion phenomenon of each

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80 wt.-%82.5 wt.-%

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Crystal by Kondrikov et al.

Line

ar b

urni

ng ra

te (m

m/s

)

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50

500

Figure 2. Linear burning rates of 95-80 wt% aq. solutions

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(a) 95 wt.% (b-1) 80 wt.% at low rb (b-2) 80 wt.%at high rb

Figure 5. The combustion waves at constant burning rate (15mm/s)

region was observed at a constant pressure, 3MPa. The photos of combustion waves are shown in Fig. 4. A two-phase region is generally observed in the combustion wave. The gas-phase is brown, which may be evidence of NO2 generation. In the case of the 95 wt.% HAN aqueous solution (Fig. 4 (a)), the liquid phase, two-phase region, and gas phase are layered in the combustion wave, and brown bubbles are observed in the two-phase region. The burning rate is low, about 3 mm/s, and the combustion wave propagates with vibration. In the case of 80 wt.% (Fig. 4 (b)), the burning rate is high, about 300mm/s, and many fine bubbles are observed in front of the combustion wave. In the case of the 85 wt.% HAN aqueous solution, two modes appear alternately. The first mode (Fig. 4 (c-1)) shows the slow burning rate, less than 3mm/s, and fine and transparent bubbles are observed in the vicinity of the interface between the liquid and gas-phase. This mode seems to be similar to the combustion phenomena of the 95 wt.% aqueous solution. The second mode (Fig. 4 (c-2)) follows the first one. The

brown bubbles grow very rapidly and the surface regression rate is very high, more than 100mm/s, however, the combustion wave structure is different from the 80 wt.% aqueous solution - fine bubbles are not observed. The first mode maintains for 500-600 ms, and the second mode for about 100 ms. Overall, the burning rate of the 85 wt.% HAN aqueous solution is 10-20 mm/s on average. Additionally, observations were made for 95 and 80 wt.% aqueous solutions at approximately 15mm/s of linear burning rate. (Fig. 5) In the case of 95 wt.% at around 7 MPa (Fig. 5 (a)), the combustion wave structure was nearly same as that at 3MPa (Fig. 4 (a)). The combustion wave of 80 wt.% at 1.5 MPa (Fig. 5 (b-1), (b-2)) shows the same two modes which are observed in the case of 85 wt.% HAN aqueous solution at 3 MPa (Fig. 4 (c-1), (c-2)).

(a) 95 wt.% (b) 80 wt.t% (c-1) 85 wt.t% at low rb (c-2) 85 wt.% at high rb

Figure 4. The combustion waves of each solution at constant pressure (3MPa)

Figure 3. Linear burning rates of 80-50 wt% aq. solutions

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50 wt.-%64 wt.-%77.5 wt.-%80 wt.-%64mass% by Kondrikov et al.

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D. Temperature Profile Temperature profiles of 95, 85, 80 and 64 wt.% aqueous solutions at around 3 MPa are shown in Fig. 6. The

origin in the x-axis denotes the point where the temperature rises from the initial temperature. As shown in Fig. 6 (a), in the case of the 95 wt.% HAN aqueous solution exhibiting a low burning rate, the temperature rises gradually from initial value and the rise suddenly stops at the certain temperature, around 500 K, which probably corresponds to the boiling temperature of the solution; then the boiling temperature is maintained for a while, and finally it increases to about 700 K. In the cases of other traces of high burning rate, as shown in Fig. 6 (b)-(d), the 85, 80 and 64 wt.% solutions, the temperatures increase to each boiling temperature as in the case of the 95 wt.% solution, and then remains nearly constant.

III. Discussion

A. Combustion Mode From the results of the observation in the wide ranges of pressures and HAN concentrations, it is found that the

linear burning rates are classified by three types. The first one, as in the case with 95 wt.% HAN aqueous solution (Fig. 4 (a), Fig. 5 (a)), is that the combustion wave shows a layered structure (liquid layer, two-phase layer and gas layer). The second one, as in the case with 80 wt.% aqueous solution (Fig. 4 (b)), is that many fine bubbles are generated in the front of the combustion wave, which propagates rapidly. The third type, as in the case with 85 and 80 wt.% aqueous solution at a low burning rate (Fig. 4 (c-1), (c-2), Fig. 5 (b-1), (b-2)), is where the two modes of combustion wave propagation appear alternately. These three types are called as Zone 1, Zone 2 and Zone 3 respectively, as shown in Fig. 7.

0 5 10 15300

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T /

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Tem

pera

ture

T /

K

(a) 95 wt. % solution (rb=3.1 mm/s, 2.9 MPa) (b) 85 wt.% solution (rb=142 mm/s, 3.2 MPa)

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Distance x / mm

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Tem

pera

ture

T /

K

(c) 80 wt.% solution (rb=654 mm/s, 2.2 MPa) (d) 64 wt.% solution (rb=395 mm/s, 3.2 MPa)

Figure 6. Temperature profiles of the combustion waves of each sample

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50mass%64mass%77.5mass%80mass%82.5mass%85mass%95mass%

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Zone 3

Zone 2

Zone 1

Figure 7. Correlation of linear burning rates and combustion types

B. Combustion Wave Structure Based on the temperature profiles of

the combustion wave, two types of combustion wave structures are proposed as shown in Fig. 8. In the case using 95 wt.% HAN aqueous solution (Fig. 8 (a)), the temperature rises gradually from its initial value, is kept at boiling temperature (Tbp) in the two-phase region, and the water vaporizes completely. Temperature increases in the gas phase until it reaches the flame temperature. This structure may be established in the case of low water content. When 80 wt.% solution is utilized, as shown in Fig. 8 (b), the temperature rises from the initial value and is kept at boiling temperature, as in the case with the 95 wt.% solution. However, the two-phase region becomes longer than in the wave structure proposed when using 95 wt.% solution, due to the higher water content; consequently, the chemical reaction in the bubbles may proceed further.

The physicochemical images of the combustion phenomena of Zone 3 (Fig. 7) are illustrated in Fig. 9. Figure 9 (i) shows stable combustion wave propagation, and (ii) shows the occurrence of stronger turbulence at the interface between the gas and the two-phase region, and that the reactive gases are concentrated in the concave area (iii). These gases react rapidly and expand vigorously into liquid phase (iv). Reactive gases are consumed completely and the thrust for the further propagation of this concave area disappears - the combustion wave structure is recovered through (v) to (i). The interface between the gas and the two-phase region is essentially unstable, and the motion shown in Fig. 9 is caused by local disturbance.

T

Tbp

Tf

Liquid phase Gas phase Two-phase

Reaction zone Reaction zone

T

Two-phase Liquid phase

Tbp

(a) 95 wt.% solution (rb=3 mm/s) (b) 80 wt.% solution (rb=650 mm/s) Figure 8. Combustion wave structure

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Reaction zone

Two-phase Liquid phase

Figure 10. Combustion wave structure at high burning rate

C. Rate of Vapor Nucleation11 Superheat, which is the difference between the gas temperature in bubbles and water temperature, probably Tbp,

increases with the chemical reaction progress in the bubbles, and generates the vapor nuclei in the vicinity of the interface between liquid and gas phases. The nucleation rate increases exponentially with superheat and pressure. For example, significant nucleation rates between 109 and 1013 m-3s-

1 correspond to a very narrow range of gas temperatures from 224 to 225.2 °C for benzene (boiling temperature; 80.1 °C). In this case, when the superheat exceeds a certain critical value for each aqueous solution, the nucleation rate increases abruptly in the two-phase region. The proposed combustion wave structure shown in Fig. 8 (b) can not be established, and a very large number of nuclei may be formed rapidly in the two-phase region as shown in Fig. 10. This rapid nucleation makes the apparent burning rate extremely high.

The estimated nucleation rate, dn/dt, is expressed in Eq. (1). Here, λ is a collision frequency, N is a constant approximately equal to the number of molecules per unit volume, k is the Boltzmann constant, Tg is vapor temperature in the bubble,

gkTrGNedtdn )( *∆−= λ (1)

and ∆G(r*) is given by

σπ **

34)( rrG =∆ (2)

where σ is surface tension of the aqueous solution and r* is the radius of the spherical vapor nucleus, which is calculated with the following formula. R; universal gas constant, TSAT; saturation temperature, ifg; latent heat of vaporization, M; molecular weight, pf; pressure in liquid phase, ∆T; superheat, Tg-TSAT.

(i) (ii) (iii) (iv) (v)

Figure 9. The transition of two mode

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1E-501E-471E-441E-411E-381E-351E-321E-291E-261E-231E-201E-171E-141E-111E-081E-051E-021E+011E+04

1 10

Pressure (MPa)

dv/d

t (m

3 /s)

Tg=1100K Tg=900K

Tg=1000K

2 3 4 5 6 7 8 9

Tg=800K

Tg=1200K

Tg=1300K

Figure 11. Increase rate of bubble volume

Table 1. Compositions of propellant solutions. Unit is mass ratio.

HAN AN H2O CH3OHControl 95 5 8 0 SHP069 95 5 8 8 SHP163 95 5 8 21

TMpiRTr

ffg

SAT

∆=

σ2* 2

(3)

The nucleation rates of pure water are calculated as functions of pressure and gas temperature (Tg) in bubbles with these formulas. Minimum radius of the vapor nucleus (r*) is set at 2 nm according to Matsumoto 12 . Further, dn/dt is multiplied by the nucleus volume, and dv/dt, the increase in the rate of nucleus volume per unit volume by nucleation, is obtained as shown in Fig. 11. As this figure illustrates, the dependency of dv/dt on pressure is same as the linear burning rates of the aqueous solution. dv/dt is directly related with linear burning rate by dividing by unit area, and for example, 10-2 m3/s of area corresponds 10 mm/s of linear burning rate. Therefore, the assumption that the nucleation process governs the linear burning rate may be supported by this result. In the case of 85 and 82.5 wt.% aqueous solutions, the gas temperature of bubble in the two-phase region may be lower than that in the 80 wt.% aqueous solution, as the two-phase region is shorter. The superheating may be less and, therefore, the nucleation and apparent burning rates lower. In the 77.5, 64 and 50 wt.% solutions, the gas temperature in the bubbles may be lower than that in the 80 wt.% aqueous solution because of higher water content of these solutions. Due to the diminished superheating, the nucleation and burning rates become lower.

IV. Propellant solution In previous study, the linear burning rates of

propellant solutions which include HAN, AN, H2O, and methanol were measured and are shown in Fig. 12. The compositions of propellant solutions are listed in table 1. As shown in the Fig. 12, the Control and SHP069 have apparently two regimes. At a certain critical pressure, the burning rate jumps from a moderate rate to an extremely high rare. The high burning rate mechanism of aqueous solutions can be applied to the propellant solutions at high pressures, however the jump of burning rate to very high region can not be explained with the combustion mechanism of aqueous solutions. Hydrodynamic instability is incorporated successfully to explain these phenomena.

A. Hydrodynamic instability Margolis9 extended the Landau/Levich instability

theory of liquid propellant by addition of the reactive/diffusive instability and applied the extended theory to HAN-based liquid propellant. In the Margolis model, the hydrodynamic instability was evaluated with the pressure sensitivity, Ap, which is shown in Eq. (4). Density ratio, ρ, is defined as the ratio of unburned liquid density, ρl, to burned gas density, ρg (ρ=ρg /ρl). σ is surface tension and Fr is Froude number.

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LIN

EAR

BU

RN

ING

RA

TE /

mm

/s

PRESSURE / MPa5 73

Figure 12. burning rate of the propellant solutions

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12

21 −+−≈ FrAp σρρ (4)

If the Ap is less than the critical value which is determined by density ratio, surface tension, viscosity, Prandtl number, Froude number, and wave number, the combustion wave is stable. Thus, smaller Ap is favorable as for the hydrodynamic instability. The Ap of our solutions are shown in Fig. 13. Ap decreases with the increase of the pressure and increases with the increase of the methanol content, which have inverse tendencies to our results.

Therefore, another mechanism is necessary for this instability. Lewis number effect was eliminated at first because Lewis number has no dependency on pressure, and the effect of flame stretch was taken account of. Markstein number is used to correlate the effect of the stretch to Karlovitz number as in Eq. 5.

KaMaS

SS

lu

sulu ⋅=−

)(

)()( (5)

Kitagawa et al. 13 obtained the characteristics of the flame instability as a function of the pressure and the Markstein number. They reported that the hydrodynamic instability was suppressed when the Markstein number was relatively large. In this paper, the Markstein number is calculated with Eq. (6), which was indicated as an asymptotic solution by Clavin et al14. In Eq. (6), β is Zel’dovich number, which is calculated by Eq. (7), where Ts is surface temperature of condensed phase, Td is activation temperature of mass diffusivity in condensed phase, Tad is adiabatic flame temperature, and T0 is initial temperature.

( ) ( )dx

xxLeMa ∫

− +−

−+

−= ρ

ρ

ρρβ

ρρ

1

0

1ln12

11ln1

1 (6)

( )

20

s

add

TTTT −

=β (7)

The hydrodynamic instability of our propellant solutions is estimated with the Markstein number and the

pressure dependency of Markstein number of each solution is shown in Fig. 14. The Markstein number decreases with the increase of pressure and increases with the decrease of methanol content. Thus, these results support the observed phenomena that the combustion wave is unstable at higher pressure than the critical pressure and the methanol addition shifts the critical pressure to higher pressure. Markstein numbers at the critical pressure are nearly same value, which is defined as critical Markstein number, Ma(cr). Although the critical pressure of SHP163 is not clear, the combustion wave structure changed at the critical Markstein number as shown in Fig. 15. Therefore, the hydrodynamic instability is affected by flame stretch and determines the critical pressure where the linear burning rate of propellant solutions jumps to high rate region.

-0.009

-0.008

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

0 2 4 6 8 10 12

Pressure sensitivity Ap

Pressure (MPa)

Control

SHP069

SHP163

Figure 13. Estimation of hydrodynamic

instability with the Margolis model

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As the pressure increases, Ma decrease and

combustion wave is more unstable, and the motion of gas phase flow is more energetic. At the Ma(cr), hot gases start to invade the liquid zone and the induced local superheat becomes the trigger of the very high apparent burning rate.

V. Conclusion The measurement of linear burning rates and

temperature of the combustion wave, and the observation of combustion phenomena, were conducted with hydroxylammonium nitrate aqueous solution. The linear burning rate has a peak at approximately 80 wt.% of HAN concentration. The combustion phenomena depend on composition and pressure, and can be classified in three types. Temperature measurements indicate that the role of the two-phase region is very important. Based upon these results, two types of combustion wave structure are proposed. The structure of 95 wt.% aqueous solution of Zone 1 is layered, and has the reaction zone in the gas phase. This structure is established in the case of low water content. In the case of 80 wt.% aqueous solution of Zone 2, the reaction zone may be in the two-phase region, and the rapid nucleation by the superheat causes a high burning rate. In the case of Zone 3, high and low burning rate modes appear alternately, and the high burning rate may be caused by the disturbance of the interface. The gas temperature in bubbles of the two-phase region and the water content of a particular solution may determine the combustion wave structure and the linear burning rate. In the case of propellant solution, the high burning rate mechanism of aqueous solutions can be applied to the propellant solutions at high pressures, however the jump of burning rate to very high region cannot be explained. Hydrodynamic instability is incorporated successfully to explain these phenomena. The stability criteria of the Margolis model did not meet our data, and the effect of flame stretch on the hydrodynamic instability is estimated with Markstein number. The estimation results support the observed phenomena that the hydrodynamic instability occurs at higher pressure than the critical pressure and the methanol addition shifts the critical pressure to higher pressure. The Markstein number where the burning rate of each propellant jumps to the very high region is same and is defined as the critical value. The factor determining the burning rate region is the bubble nucleation rate in the case of aqueous solutions and is the hydrodynamic instability in the case of propellant solution.

Reference 1 Harlow, D.G., Felt, R.E., Agnew, S., Barney, G.S., McKibben, J.M., Garber, R., and Lewis, M., “Technical Report on Hydroxylamine Nitrate,” Department of Energy, U.S., DOE/ EH-0555, 1998. 2 Togo, S., Shibamoto, H., and Hori, K., “Improvement of HAN-Based Liquid Monopropellant Combustion Characteristics,” Proceeding of International Conference HEMs-2004 [online proceeding], URL: http://frpc.secna.ru/hems-2004/f08.rar [cited Oct. 25, 2009]. 3 Vosen, S.R., “Concentration and Pressure Effects on the Decomposition Rate of Aqueous Hydroxylammonium Nitrate Solution,” Combust. Sci. and Tech., 6, 1989, pp.85-99. 4 Vosen, S.R., “Hydroxylammonium Nitrate-Based Liquid Propellant Combustion,” Combustion and Flame, 82, 1990, pp.376-88.

(a) Ma>Ma(cr) (b) Ma<Ma(cr) Figure 15. Difference in combustion wave

structure of SHP163

33.5

44.5

55.5

66.5

77.5

8

0 1 2 3 4 5 6 7 8 9 10 11

Markstein number

Pressure (MPa)

ControlSHP069SHP163

Ma(cr)

Figure 14. Dependency of Markstein number on pressure

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5 Chang, Y.P., and Kuo, K.K., “Assessment of Combustion Characteristics and Mechanism of a HAN-Based Liquid Monopropellant,” 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper No. 2001-3272, 2001. 6 Chang, Y.P., Josten, J.K., Zhang, B.Q., Kuo, K.K., and Reed, B.D., “Combustion Characteristics of Energetic HAN/Methanol-Based Monopropellants,” 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper No. 2002-4032, 2002 * Lee, H.S., and Litzinger, T.A., “Chemical Kinetic Study of HAN Decomposition,” Combustion and Flame, 135, 2003, pp.151-69. 7 Katsumi, T., Kodama, H., Shibamoto, H., Nakatsuka, J., Hasegawa, K., Kobayashi, K., Ogawa, H., Tsuboi, N., Sawai, S., and Hori, K., “Combustion Characteristics of HAN-Based Liquid Monopropellant,” International Journal of Energetic Material and Chemical Propulsion, Vol.7, 2, 2008, pp. 123-137. 8 MARGOLIS, S.B., COMBUSTION AND FLAME, 113, 1998, pp.406-423. 9 Kondrikov, B. N. et al., (2000) Burning of Hydroxylammonium Nitrate, Combustion, Explosion, and Shock Waves, Vol.36, No.1, pp.135-145. 10 Collier, J. G. and Thome, J. R., Convective Boiling and Condensation, Oxford University Press, New York, NY, 1994, pp.135-138. 11 Matsumito, M., “Surface Tension and Stability of a Nanobubble in Water: Molecular Simulation,” J. Fluid Science and Technology, Vol.3, No.8, 2008, pp.922-929. 12 Kitagawa, T., Ogawa, T., and Nagano, Y., “Effects of Pressure on Instability and Cellularity of Propagating Spherical Laminar Flames,” Journal of the Japan Society of Mechanical Engineers, Series B, 70(698), 2004, pp.2649-2656. 13 Clavin, P., and Williams, F.A., “Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity,” Journal of Fluid Mechanics, 116, 1982, pp. 251-282